Lab Report

Iqra Qumar

March 21, 2019

The Devil’s Number:

The Probability of Rolling Dice

ABSTRACT

            In this experiment, I rolled two dice 100 times. This experiment was done to see what outcomes occur each time that the dice is rolled. Rolling dice is not hard, but I found an easy way to do it. To do this experiment, I used a code that I created in my senior year of high school in C-sharp. In this code, I gave the user the chance to roll one die or two dice through a random generator that the computer outputted. Then, I recorded the results in a table and noticed that six had the highest outcome once the two dice were added together.

INTRODUCTION

             Everyone has played with dice at least once in their life. It is in games like Monopoly, The Game of Life, Candyland, etc. It is all about luck and chance. You do not know where it will land so you have no idea if you will win or not. This experiment is to roll two dice and record the outcome. I recorded each time I rolled the dice and added them together to get the resulting number. This is the number I used to prove which number is rolled the most amount of times. The reason for this experiment is to test probability and see if the dice favors any numbers. We all know that dice are random, however, the number six is the most common number that results after being rolled.

MATERIALS AND METHODS

If you are going to be coding the experiment, you will need:

  • Skills in C-Sharp
  • Visual Studio 2017 program
  • Create a code that asks the user to decide if they want the computer to roll one die or two dice.
  • Choose your option (two dice for faster result).
  • Record number that is outputted in table.
  • Add the two numbers together to get total amount.
  • Determine which number is outputted the most from results.

If you are going to be doing this in real life, you will need:

  • 2 dice
  • A chart to record your outcomes
  • Possibly a friend to help out
  • Roll the two dice.
  • Record the number on each die in table.
  • Add the two numbers together to get total amount.
  • Determine which number is outputted the most from results.

RESULTS

            As stated in the abstract, my common result was the number six. It appeared 21 times in different combinations such as 3 and 3, 2 and 4, and 5 and 1. The numbers were flipped at times because I did use a code to do it, so the computer generated the numbers in the order it wanted to.

Table 1. The numbers that occurred in every roll and the sum of the two dice.

Results of the Sum of Two Dice

Sum of Dice Times Rolled
1 0
2 6
3 7
4 9
5 13
6 21
7 16
8 5
9 16
10 3
11 2
12 2

Fig. 1. Bar graph of the results when the two dice results were added together to show which outcome is more common.

            Figure 1 helps to put Table 1 into a visual, so we have a better idea of what type of results this experiment has given.

ANALYSIS

            When observing both Figure 1 and Table 1, we can see that the sum of six was rolled 21 times. This was followed by seven and nine, which both numbers appeared 16 times. This proves my hypothesis to be true because six was the most common outcome during the 100 times I rolled the dice. This is probably the result because it is the sum of half the number you can get while doing this experiment. What I mean is that the two dice add up to 12. Since six is half of that number, it is more likely to appear. Moreover, it is very uncommon for bigger numbers such as 11 and 12 to appear regularly because it is rare for both of the dice to output a large number at the same time. Most of the time the dice output small numbers and that is how you get the results that I got while experimenting. You can refer to the appendix for further details of each roll.

            In another experiment conducted by Sandra Hanson McPherson, she used a game called Unders and Overs to find out the probability of rolling two dice. Her hypothesis was that the result would be either less than seven, equal to seven or greater than seven. She made her students choose one outcome and based her results on those three choices. Her results were that 15/36 times the sum of the dice was over or under seven, while the probability of getting exactly seven was 1/36 [McPherson, 2015]. McPherson had a larger basis for her hypothesis, which is why her results are different from mine. She was going to get a right answer no matter what, whereas my results were restrained to a single number. Her hypothesis was going to be correct no matter what, but mine depended on a single number. That is where our results vary for the same type of experiment.

CONCLUSION

            I conducted an experiment with the use of a code that helped me roll two dice. Once the dice were rolled, I added them together to get my data. The results supported my hypothesis that six is in fact the most common sum of two dice. It appeared 21 times out of the 100 times I did this experiment. Six appeared the most because it is right in between the largest number that could possibly occur. Moreover, most dice output smaller numbers and that is what most of my results were.

REFERENCES

McPherson, S. H. (2015). Unders and Overs: Using a Dice Game to Illustrate Basic Probability Concepts. Teaching Statistics, 37(1), 18–22. https://doi-org.ccny-proxy1.libr.ccny.cuny.edu/10.1111/test.12033

APPENDIX

Code Used:

using System;

using System.Collections.Generic;

using System.Linq;

using System.Text;

using System.Threading.Tasks;

namespace RandomGenerator

{

    class Program

    {

        static void Main(string[] args)

        {

            menu();

        }

        static void leading()

        {

            Console.BackgroundColor = ConsoleColor.DarkMagenta;

            Console.ForegroundColor = ConsoleColor.Cyan;

            Console.Clear();

            Console.WriteLine(”                              Random Generator”);

            Console.WriteLine(“”);

        }

        static void menu()

        {

            int choice;

            leading();

            Console.WriteLine(“Menu:”);

            Console.WriteLine(“For DICE (one or two), please press 1.”);

            Console.WriteLine(“To EXIT the game, please press 2.”);

            Console.WriteLine(“Please input a number from 1-2.”);

            choice = int.Parse(Console.ReadLine());

            switch (choice)

            {

                case 1:

                    dice();

                    break;

                    menu();

                    break;

            }

            Console.ReadLine();

        }

        static void dice()

        {

            leading();

            Console.WriteLine(“DICE MODE”);

            Console.WriteLine(“”);

            Console.WriteLine(“Menu:”);

            Console.WriteLine(“For one die, please press 1.”);

            Console.WriteLine(“For two dice, please press 2.”);

            Console.WriteLine(“To go back to main menu, please press 3.”);

            Console.WriteLine(“”);

            Console.WriteLine(“Please input your choice.”);

            int rand;

            int rand1;

            int rand2;

            int roll = int.Parse(Console.ReadLine());

            if (roll == 1)

            {

                leading();

                Random random = new Random();

                rand = random.Next(1, 6);

                Console.WriteLine(“Press enter for me to roll a fair die!”);

                Console.ReadLine();

                Console.WriteLine(“The number rolled was ” + rand);

                Console.WriteLine(“”);

                Console.WriteLine(“To go back to dice menu, please press enter.”);

                Console.ReadLine();

                dice();

            }

            else if (roll == 2)

            {

                leading();

                Random random = new Random();

                rand1 = random.Next(1, 6);

                rand2 = random.Next(1, 6);

                Console.WriteLine(“Press enter for me to roll a fair dice!”);

                Console.ReadLine();

                Console.WriteLine(“The first number rolled was ” + rand1);

                Console.WriteLine(“The second number rolled was ” + rand2);

                Console.WriteLine(“”);

                Console.WriteLine(“To go back to dice menu, please press enter.”);

                Console.ReadLine();

                dice();

            }

            else

            {

                menu();

            }

            Console.ReadLine();

        }

        static void exit()

        {

            Console.WriteLine(“If you want to exit the game, please press 1.”);

            Console.WriteLine(“If you want to go to the menu, please press 2.”);

            int choice = int.Parse(Console.ReadLine());

            switch (choice)

            {

                case 1:

                    Environment.Exit(0);

                    break;

                case 2:

                    menu();

                    break;

                default:

                    menu();

                    break;

            }

        }

    }

}

Data of Dice for Table 1 and Figure 1:

Dice 1 Dice 2 Total
4 3 7
1 1 2
2 1 3
4 5 9
5 5 10
3 5 8
5 2 7
4 1 5
2 2 4
3 3 6
4 5 9
1 2 3
5 4 9
2 4 6
3 3 6
2 4 6
1 2 3
5 1 6
4 4 8
4 2 6
1 1 2
2 1 3
5 4 9
2 5 7
1 5 6
3 5 8
1 3 4
4 1 5
3 1 4
5 4 9
1 2 3
5 2 7
1 4 5
4 5 9
5 2 7
3 1 4
1 1 2
5 1 6
4 3 7
5 4 9
3 4 7
2 3 5
4 5 9
2 4 6
1 5 6
6 6 12
2 5 7
1 4 5
3 4 7
2 3 5
4 2 6
4 1 5
4 5 9
2 2 4
5 4 9
5 4 9
2 2 4
1 4 5
1 2 3
2 3 5
5 4 9
2 5 7
4 5 9
1 1 2
5 1 6
5 5 10
4 5 9
1 1 2
3 1 4
1 5 6
4 4 8
4 3 7
1 4 5
5 1 6
4 2 6
1 3 4
2 4 6
5 2 7
4 5 9
5 1 6
1 4 5
5 4 9
5 3 8
3 1 4
2 4 6
4 3 7
1 4 5
3 4 7
4 2 6
2 1 3
5 5 10
5 6 11
4 2 6
6 6 12
4 1 5
3 4 7
5 1 6
1 1 2
5 6 11
2 5 7